BER AWGN example - question

GNU Radio
1

Dear GNU Radio users,

I have just read the tutorial about simulations in GNU Radio
(http://gnuradio.org/redmine/projects/gnuradio/wiki/Simulations) and I
would be grateful if you could help me with understanding part of it.

Could you explain how the converting the EbNo value to the noise
voltage in the following example is done?
http://gnuradio.org/redmine/projects/gnuradio/repository/entry/gr-digital/examples/berawgn.py

I can see that there is a function (EbNo_to_noise_voltage) responsible
for that but I have problem with understanding where this equation came
from. Could you possibly explain it to me or at least recommend some
book where I can find the solution?

Best Regards,
Piotr Bieńkowski

2

On Sat, Dec 07, 2013 at 02:26:18PM +0100, [email protected]
wrote:

Could you explain how the converting the EbNo value to the noise
voltage in the following example is done?

http://gnuradio.org/redmine/projects/gnuradio/repository/entry/gr-digital/examples/berawgn.py

I can see that there is a function (EbNo_to_noise_voltage)
responsible for that but I have problem with understanding where
this equation came from. Could you possibly explain it to me or at
least recommend some book where I can find the solution?

Given an E_b of 1, what is the noise voltage (i.e. the expected
amplitude of the AWGN process) that will cause an E_b / N_0 of x, if E_b
/ N_0 is given in dB?
If you take pencil and paper, and solve for the noise voltage, you’ll
get this equation.

MB

–
Karlsruhe Institute of Technology (KIT)
Communications Engineering Lab (CEL)

Dipl.-Ing. Martin B.
Research Associate

Kaiserstraße 12
Building 05.01
76131 Karlsruhe

Phone: +49 721 608-43790
Fax: +49 721 608-46071
www.cel.kit.edu

KIT – University of the State of Baden-Württemberg and
National Laboratory of the Helmholtz Association

3

Martin B. (CEL) wrote

Given an E_b of 1, what is the noise voltage (i.e. the expected
amplitude of the AWGN process) that will cause an E_b / N_0 of x, if E_b
/ N_0 is given in dB?
If you take pencil and paper, and solve for the noise voltage, you’ll
get this equation.

Thank you very much for your reply. I am capable of simple converting
value
in [dB] to the one in [W/W] but I don’t know why there are the
number_of_bits_per_symbol parameter and the ‘2’ constant in the
equation.
It’s probably trivial but I would really appreciate your help on this.

Best Regards,
Piotr Bieńkowski

–
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Sent from the GnuRadio mailing list archive at Nabble.com.

4

Thank you very much :slight_smile:

BR,
Piotr Bieńkowski

–
View this message in context:
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Sent from the GnuRadio mailing list archive at Nabble.com.

5

On Mon, Dec 09, 2013 at 03:10:49AM -0800, bieniu wrote:

It’s probably trivial but I would really appreciate your help on this.
The number_of_bits_per_symbol is for E_s -> E_b conversion and the 2 is
for two-sided noise power to one-sided conversion (or was is the other
way 'round? I always mix those up :).

MB

–
Karlsruhe Institute of Technology (KIT)
Communications Engineering Lab (CEL)

Dipl.-Ing. Martin B.
Research Associate

Kaiserstraße 12
Building 05.01
76131 Karlsruhe

Phone: +49 721 608-43790
Fax: +49 721 608-46071
www.cel.kit.edu

KIT – University of the State of Baden-Württemberg and
National Laboratory of the Helmholtz Association